So Jimmy (the collective name for his brains) has this one-in-a-handwavium-amount blessing/curse. Instead of one central brain, his head, each arm, each leg, and his torso have independently operating brains. Each brain wants to do what’s best for it’s part of the body. The legs can move the body, the arms can manipulate things, his head controls sensory input listens (somewhat) to the torso, and the torso thinks a lot and controls involuntary muscles. The torso also controls the cross-brain communication. If a limb brain was killed, the limb loses control and is dead weight. If the head brain is killed, sensory deprivation, loss of intake and speech occurs. If the torso brain is killed, the involuntary muscles and cross-brain comms are down. How are Jimmy’s brains going to coordinate actions if they don’t want to do something (e.g. the legs don’t want to move because their tired, or the torso doesn’t want to cross communicate), and how will Jimmy(as a collective conscious) survive?
Jimmy is a human octopus/arthropod.
Jimmy over here is a pretty special fellow, for his species, because unlike humans, whose brains are pretty centralized and coordinate essentially all bodily functions, Jimmy's nervous system works in a way closer to that of an arthropod or cephalopod, in that his nervous system does not have one central brain doing the absolute majority of everything brain-related. Instead, Jimmy's nervous system is divided in at least 6 different ganglia connected together. This isn't all that crazy, nor is it something with no precedents. Let's look at 2 great examples:
Roaches have 2 "brains", in that one in the torso handles mostly bodily functions while the one in the head deals with processing information, remembering stuff and keeping the roach alive and healthy. A brain in your torso is essentially plausible. It's because of this arrangement (as well as the open circulatory system) that a cockroach can survive without its head. It can survive, but without the head it will die, as it can't eat, drink or really see (though it can kinda still sense its way around).
Octopuses on the other hand take this to another level: only 1/3 of an octopus' neurons are in its head and body, the remaining 2/3 being distributed between its 8 arms. Essentially, octopuses have 9 "brains" or ganglia, with the central one handling the head, body and coordinating everything while the other 8 each handle a single limb. As a result of this, you can see cut off arms searching for Food and trying to bring it to where the mouth would normally be. This, as well as their fluid shape, also means octopuses have no body map, aka they couldn't touch an arm with another with their eyes closed.
Now if I understand correctly, Jimmy's nervous tissue arrangement, at least in the base connections between extremities, all work like a medula, in that rather than just going into the limb, they converge into the ganglia like our spinal cord does to our brain. This is why if the brain dies, the nerve impulses can no longer pass through, and thus the limb remains unresponsive, not unlike in the case of a paraplegic.
With Jimmy's nervous system covered in roughly how it is based on these 2 animals, let's talk about the biggest problems: excessive indepence and the current distribution of functions.
1- function distribution.
his head controls sensory input listens (somewhat) to the torso, and the torso thinks a lot and controls involuntary muscles.
This over here could easily become a death sentence for any regular animal. Bilateral creatures (with one side of the body mostly mirroring the other in terms of limbs etc) usually have a head where the bulk of the sensory organs are. At the same time, this is usually where most of the thinking ganglia or brain is. Why? Because overall having your eyes and the place that processes what the eyes see and how to react based on it makes the whole process a lot faster, meaning a shorter reaction time. Both roaches and octopuses show this, as both have the brain coordinating the body in the "head" region close to the eyes. What about Jimmy? Jimmy's main "thinking" brain is in his torso, entirely restricted to a sense of touch and relying entirely on the good will of the head region to share this. What does this all entail? That living in a civilized society is the only reason Jimmy is still alive.
Remember how I said the brain handles most of the brain jobs (like moving the body and telling each organ what to do)? Thing is the spine plays a role in this too: when our limbs send a signal of pain back to the brain, say because you're touching something hot, your spine kicks in and automatically sends a signal for you to move the limb away from what's causing the issue. This is known as a reflex action, and can occur even in paraplegic and tetraplegic people, as the brain plays no part in this. Why does this exist? Because if the spine didn't handle the reaction, the signal would need to travel all the way to the brain, be interpreted as "ouchie we're burning our hand" and cause a "well stop touching it" signal to be sent back, and during this extra time you'd be getting a bad burn.
Jimmy's senses work in the way a reflex action would work without the spinal cord acting: the head brain gotta receive the sight signal of, say, a rabid animal running towards him, interpret the signal, resend the signal to the torso brain, be interpreted again and THEN result in a "let's run" signal to be sent. This extra time to react could easily cost Jimmy his life.
Essentially, we're already starting out wrong. For Jimmy to have a better chance of surviving in general, he needs the head brain to handle the bulk of decision-making, while the body troubles itself with its own functions first (like making sure Jimmy keeps breathing, or that digestion keeps happening). The torso brain can have the ability to control the body, but the head needs to have priority. If Jimmy gets beheaded and somehow survives, then we start letting the torso play big boss.
And speaking of priorities, we go on to the second glaring problem:
2- the individuality issue.
As you described it, it's no wonder Jimmy's condition is so rare: it's a death sentence for anything that has to worry about predators or catching food outside of going to the market.
Roaches, octopuses and many other invertebrates have their nervous system divided in ganglia, octopuses here being the best comparison as their arms can actually act fully independently from the body. What's the problem with Jimmy that we don't find in the octopus? Simple: Octopuses' limbs are independent, but not human-independent.
You see, our bodies at their core are a collection of cells, which work all in unison in a bunch of different ways, resulting in one animal that's better at staying alive than if the cells all tried to act independently. True independence does not work in multicellular creatures. In fact, when a cell starts to act independently and focusing solely on its own survival and reproduction independently from the collective, you get what we know as "cancer".
Same thing for, say, an ant hive: each and is its own animal, capable of thinking and acting on its own, yet it performs according to the hive, and will even March towards its death in order to defend it. Why? Because by their singular sacrifices, the collective can keep living, just like our skin cells made to die and act like a shield to the rest of our bodies.
Jimmy as you described on the other hand is not like an octopus or an ant colony or even a cluster of cells acting like one animal, Jimmy's brains is each have their own wants and needs,and that again means that a society structure is the only reason Jimmy can survive. If Jimmy's legs decided to stop moving for being tired while he still needed to run from a threat, he'd die. If Jimmy's arms decided to not let Jimmy grab food, he'd starve. If Jimmy's head didn't share anything with the body because they had a fight, Jimmy would be defenseless against the environment.
So as of now, Jimmy might be able to survive, just like a family of 6 can learn to work together, but only because he lives in a society. Jimmy may have faster reaction time and finer motor control on each limb, but his reaction time in terms of sight, hearing, smell or taste are slower. If Jimmy has an inner fight, it can cause his death, and Jimmy is overall much less coordinated than an octopus, which technically has more brains than Jimmy.
This becomes extra important when you remember intelligent creatures can and do become depressed and commit suicide. If Jimmy's body becomes depressed and stops doing its works, Jimmy would die. If Jimmy's limbs do it, his chances of surviving become much worse.
This needs fixing: Jimmy can have several ganglia each meant to supervise a specific part of his body, but only one can act more like a human brain with self consciousness and independence, and it's gotta be the head so he can process all the stimuli and react to it better. Also, head needs admin privileges over the body: Jimmy's limbs can do as they please when not ordered around, but if Jimmy tells the legs to run, the legs need to stop everything and run. If Jimmy tells the arms to keep holding on even though it's going through high muscle stress, the arms need to keep holding for as long as they can. Otherwise, the torso and limbs will be doing their thing, but they all work based on a single purpose: "I want the body as a whole to stay alive, and the head knows best how to do that". Jimmy may still end up having an apple his arm found shoved into his mouth while talking to someone, because food equals good and the body needs it, but if Jimmy tells the arm to stop, it needs to stop and not become useless to the body because its feelings got hurt.
So summing up: Could Jimmy survive as a collective consciousness? Probably yes. Overall Jimmy would be a more dramatic, slightly different version of Abby and Brittany Hensel, in which rather than 2 independent brains each controlling an arm and a leg, you'd have 6 brains needing to work together to pilot the body. Learning how to cooperate and work together in harmony would be a must in order for Jimmy to be able to function like a normal person, although with ups and downs in terms of things like fine motor control and reaction time, but it's probably not impossible. Jimmy being in a society where predators aren't usually a problem and getting food is as easy as going to a convenience store would help a lot as well.
Jimmy could however have an even better life if his other 5 brains were less human-like and more instinct driven, naturally structured to do as the head commands while mostly doing their thing while not being bossed around. With this Jimmy could better enjoy the ups of finer motor control and reaction time to touch and suffer less from downs like slower reaction to visual signals, while also not having to undergo group character development and Learn that teamwork makes the dream work, or at the very least "making the dream work" wouldn't be about being able to properly walk to the kitchen and make a sandwich to eat.
(also Jimmy might be able to regrow nervous tissue like an octopus and make a new non-head ganglia if an old one dies, but that's not guaranteed).
In the most literal sense. Misbehaving regions are punished by the other members of the corpus collective, in a manner appropriate to the crime and body region. The exact nature of these punishments and the crimes for which they are meted out will be left to the author or in this case the readers imagination.
So, limbs can think. But how smart are they? We can effectively remove the limbs capability of rebelling or refusing to obey. Afterall, some of the most long-lasting governments and ideas, no matter how bad or ridicilous their rules may be, stand on people lacking ability and mindset to disobey and rebel. How? Lets try.
So, in this case, lets remove some of the safety mechanisms of limbs like "stop when tired" or "retreat when burned/hurt etc". Instead, like humans, lets add these safety stuff to a spine-like nerve structure, to remove the restriction mechanisms for safety from autonomous part of the limb and make it non-autonomous.For a normal human, reflexes and most of the safety mechanisms are controlled by spine to quicken those necessary reflexes. To keep the limb safe, to react faster, etc. And if this new 5 sided spine, is the same connection to the torso like human spine and brain connection, then all the safety mechanisms and many other halting commands are actually directly bound to torso. So, torso will have the power to control this channel to effectively override the safety measures with dedication or just pure will.
But this still won't solve the issue of "I will not work because I don't like you" mentality of limbs. So, we need to make the limbs in more primal when it comes to intelligence. A limb with the intelligence of a worm, or maybe a fish, could be better. Because, this time the limb can use its touch sense or any other sense you can add to do its job more efficiently, but restricting and safety mechanisms will strictly bound to torso but with a spine like structure to fast reaction. In this way, limbs are incapable of rebelling. It is not a question of "will they rebel?" Now it is a question of "Are they capable of rebelling?" and answer is, no. They are not capable.
This also means jimmy has effectively 6 "gut feelings". Because all the limbs have very limited survivability specialized on their own structure, their sensitivity to touch based impulses can be highly amplified.
Limited thinking, hyperspecialization
There are quite a few popular AI that makes art. You enter a small text and they give you scripts, images, etc. But those AI cannot, for example, drive a car or cook your food or run your fridge. Now, why? Because they are incapable of those actions, and their capacity is only enough for one group of tasks.
If we make the limbs minds work and act the same, then for example the right arm will try to be the best right arm it can be. And, they can be trained to become even better. To learn when to react, to learn when to take initative and to learn when to obey.
Now imagine a cluster of AIs (brains) like this, all resides in a limb. We can draw some inspiration from Asimov's rules for robots. https://en.wikipedia.org/wiki/Three_Laws_of_Robotics All limbs has a few key goals. From most important to least,
-Harmony and unity with the body,
-Survival of the main body,
You cannot be efficient if you can't survive. And you cannot survive if you can't get food from the main body. So, for following the important roles with this order, limb cannot, and definetely will not disobey. And it also can only think and perform a certain group of actions so, rebelling can only happen in something like cancer or a degenerative disease on that limb's "brain".
There is, an interesting alteration you can make. Change the order of importance. From most important to least,
-Survival of the main body,
-Harmony and unity with the body,
Now, limbs can "sacrifice" themselves to save the main body if an extreme situation occurs. They can exert force at highest level even at the cost of damaging the limb. If jimmy can regenerate these limbs and brains of those limbs, then his limbs can maybe shield the main torso, or allow him to interact with hazards to escape a dangerous situation even if the limbs get damaged.